WASHINGTON — Senator John McCain called Sunday for a special committee to investigate the administration’s handling of last year’s deadly attack on the US diplomatic post in Libya, and a House committee chairman vowed to seek additional testimony on how the matter was investigated.

The dispute over last September’s assault in Benghazi that killed four Americans dominated the network talk shows on Sunday. Leaders of both parties debated whether the administration paid enough attention to security before the attack, did enough to respond once violence began, and tried to deceive the public afterward in the midst of an election campaign.

‘‘I’d call it a coverup,’’ said McCain, a Republican from Arizona, who appeared on ABC’s ‘‘This Week.’’ ‘‘I would call it a coverup in the extent that there was willful removal of information, which was obvious.’’

McCain called for a select committee to investigate. Last week, several House Republicans called for a special investigation in that chamber as well.

Representative Darrell Issa, Republican of California and chairman of a House Oversight and Government Reform Committee investigating the episode, also referred to a coverup as he charged that the administration scrubbed talking points to falsely blame an anti-Muslim video rather than specific terrorist groups.

‘‘The American people were effectively lied to for a period of about a month,’’ he said on NBC’s ‘‘Meet the Press.’’ ‘‘They were in fact covering up an easy attack that succeeded, that was from the get-go really about a terrorist attack. It was never about a video.’’

Issa said he would deliver requests for testimony on Monday to former ambassador Thomas Pickering and Admiral Mike Mullen, the retired chairman of the Joint Chiefs of Staff, who led a State Department review of the incident.

Issa, whose committee has been leading the latest investigation in the House, said he did not believe a special investigation would be necessary.

Ambassador J. Christopher Stevens and three other US government employees were killed when the Benghazi diplomatic compound was stormed on Sept. 11. The highly charged and politically polarized debate about the episode flared up last week with congressional hearings featuring State Department officials who questioned the handling of the situation, including the failure to make any effort to intervene militarily.

Criticism was further fueled by the disclosure of drafts and e-mail messages showing how the administration directed the editing of talking points after the attack to remove references to Al Qaeda and another terrorist group, and any warnings of threats in Benghazi. The White House last week said it was trying to avoid speculation and stick to what was definitively known at the time.

Democratic lawmakers and a former Pentagon chief came to the defense of the administration on Sunday.

Former defense secretary Robert M. Gates, who served several Republican presidents in various capacities, before staying on under President Obama for 2½ years, rebutted the suggestion that the Pentagon could have scrambled jets or special forces during the attack a ‘‘cartoonish impression of military capabilities.’’

‘‘Frankly, had I been in the job at the time, I think my decisions would have been just as theirs were,’’ he said on CBS’s ‘‘Face the Nation.’’ ‘‘Frankly, I’ve heard, ‘Well, why didn’t you just fly a fighter jet over and try and scare ’em with the noise or something?’ Well, given the number of surface-to-air missiles that have disappeared from Khadafy’s arsenals, I would not have approved sending an aircraft, a single aircraft over Benghazi under those circumstances.’’

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.